Programming assignment 2 - Menger Sponge

You are to write a program to produce a a Menger sponge as shown below:

Like the Sierpinski tetrahedron in our example in class, this is a 3-dimensional fractal, defined recursively. Unlike the tetrahedron, where you think of the recursion as a subdivision of each edge of an original tetrahedron to form smaller tetrahedra, the sponge is probably best defined by recursively replacing each cube of side length s with an arrangement of cubes of side length s/3 such that the original cube's volume is nearly filled by the smaller cubes, omitting the center cube of each face and the center cube of the entire volume.

You must allow the level of recursion to be varied as in the gasket program. You should also start with this program for a Sierpinski gasket. You should change the view from the orthographic view used in this program to a perspective view. You can use a similar coloring of faces as used in this program for your cube.

You must make it possible for the user to control the drawing with a mouse-based interface and menu-based system. The recursion level along with the viewing position and any extra credit options must be controlled via mouse/menu. Here is some example source code that uses openGL and glut for a variety of functions including mouse-based control. No particular interface for the viewing position changes is required in this assignment, but you should be able to move the camera position and orientation sufficiently to be able to look at the cube from any arbitrary angle.

Oh, and be careful not to allow a user to specify a large number of recursion levels. To see why, tell me how many cubes would be required at level 5 and at level 10.

For extra credit, try one or more of these:

• Change the perspective transform parameters interactively.
• Color the faces more realistically, using a light source and shading.
• Display the "inverse sponge", the holes cut out of the Menger Sponge, as well as the sponge itself.

Notes:

• To compile this code on the departmental machines, use a command of the form:
  gcc -o gasket gasket3.c -lGL -lGLU -lglut
• If you are compiling the gasket3 code, then running it, and seeing a segmentation fault, you are probably using the gasket3.c from the book, and you are running it without giving it a recursion depth parameter. Try it with "3" as the depth parameter (e.g. "gasket3 3") and see if that fixes it. If you run the code linked above, you will not have this problem, but you will also have to remember to put #include <GL/glut.h> in for the statement #include <glut.h> to compile it under linux.